| 刘颖博.三维拟线性波方程的小初值光滑解[J].数学年刊A辑,2018,39(2):127~144 |
| 三维拟线性波方程的小初值光滑解 |
| Small Data Solutions of 3-D Quasilinear Wave Equations |
| Received:July 24, 2016 Revised:May 06, 2017 |
| DOI：10.16205/j.cnki.cama.2018.0012 |
| 中文关键词: 整体解, 零标架, 加权能量估计, 连续论证法 |
| 英文关键词:Global existence, Null frame, Weighted energy estimate, Continuous induction |
| 基金项目:本文受到国家自然科学基金(No.11371189)的资助. |
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| 中文摘要: |
| 对三维小初值拟线性波方程$\sum\limits_{i,j=0}^3g^{ij}( u)\p_{ij}u=0$, H. Lindblad 证明了它有整体光滑解.
本文考虑如下带有小初值的拟线性波方程$\sum\limits_{i,j=0}^3g^{ij}(u)\p_{ij} u=(\p u)^3$,
通过得到低阶导数的衰减估计和高阶导数的能量估计, 由连续论证法证明了这个方程也存在整体光滑解. |
| 英文摘要: |
| For the 3-D quasilinear wave equation $\sum\limits_{i,j=0}^3g^{ij}(u)\p_{ij}u=0$,
a global existence result has been shown by H. Lindblad.
This paper deals with this 3-D quasilinear wave equation
$\sum\limits_{i,j=0}^3g^{ij}(u)\p_{ij} u=(\p u)^3$ with small initial
data. Through deriving decay estimates of low derivatives
and energy estimates for high derivatives, combined with
known weighted energy inequality, a global existence
solution is also established by continuous induction. |
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